MTM5
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MrVibrating
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Re: MTM5
..just remembered - i forgot to factor in the CF-PE in Q3; the total CF-PE delta is 2 J, so 1 J per stroke, in or out; makes little difference to the results but i'll re-summarise the full cycle after auditing Q4..
@Tarsier79 - i've had multiple doubts throughout, been ready to throw in the towel several times, only to then realise the issue was my comprehension of what's happening rather than the interaction itself. Blinkered expectations, basically.
So to set the record straight - as i understand things currently:
• The interaction isn't, in and of itself, a canned energy gain, but a means of subverting N3
This in turn can be exploited to create or destroy energy.
• Whatever base inertia the interaction is mounted to - in this case the planet - becomes a functional part of the system
So a Bessler wheel-type system is going to include the Earth.
• creating or destroying energy - in the current single-wheel system at least - appears to transfer or convert the planet's spin momentum into translational momentum and vice-versa
We can watch this unfold through a cycle, and accumulate over successive cycles. I need to perform brake tests - braking the discs against one another after n cycles - to check for permanent before / after changes to the planet's resting momentum state. If there is, then this obviously needs mitigating such as by running dual opposing systems in sync and retesting until sustainable results are obtained.
This transfer of momentum between rotational and translational dimensions (ie. axial and orbital) can be clearly observed in the momentum-calibration sims i've been running this last week or so; specifically we see that the rotational angular momentum applied to the weight as it falls is balanced not only by rotational counter-momentum, but also includes a significant translational component.
So for example in Q1 where the weight falls from 0° TDC to 90°whilst being spun up in the same angular direction it's falling; if the blue disc gains 1 kg-m²-rad/s of spin about its own axis, the rotor it's riding will gain -0.666 kg-m²-rad/s of counter-rotational momentum, and -0.333 kg-m/s of translational momentum. Yes, this is mixing units and dimensions, yet they're still numerically-equivalent due to the equivalence of kg-rad/s and kg-m/s built into the metric system (the same reason both 1 kg * 1 m/s and 1 kg-m² * 1 rad/s have ½ J). This picture is obviously further complicated by the asynchronous speeds of the kiiking rotor relative to the wheel - so the absolute angles of these trans components are constantly rotating.
What it isn't is a closed-system 'black box' energy gain comprised of two or three discs - again, the closed system is only represented by including the base inertia of the system FoR. It simply cannot be closed otherwise - N3 symmetry cannot be observed in the sum of rotational momenta alone. All my attempts at doing so involved curve-fitting and fudging, massaging the figures to try and produce a desired outcome rather than a realistic one.
This is thus the same reason that what we might intuitively expect to represent the two or three-disc 'minimum system' does not reproduce the energy disunity on its own when free to accelerate and decelerate in reaction to its own internal motions - again, it's an N3 break, not a self-contained energy-gain in its own right.
To harness an N3 break into an CoE break requires applying it between two loads, an output and an input. The N3 violation here is that the counter-torques from spinning up the blue disc are not being fully commuted to the motor driving the grey disc that's causing the CF force that the counter-momentum is being sunk to over time.
In other words, in order for CoE to be satisfied, spinning up the weight in the same angular direction that it's orbiting will produce counter-torque that brakes against its orbital velocity, and the load on the central motor resisting that deceleration would be equal to the work done by the orbiting motor driving the spin-up.
Here however, that negative torque component is being vectored against CF force, which is trying to accelerate the weight's fall outwards, whilst its counter-torque is resisting that acceleration. If we didn't spin up the weight as it fell, the green disc it's mounted to would obviously be accelerated, but we've foregone that acceleration of the green rotor and instead applied it - and more - to the blue disc.
What we're really talking about in terms of force accelerations of mass over time is time rates of exchange of momentum - a passive force * displacement has a corresponding momentum value, whether the force is gravity, CF or whatever, that is a function of the drop time. Unilaterally slowing the drop (ie. kiiking) thus increases its potential momentum yield. So the final momentum we end up with, upon despinning at BDC, is more than we would've gained from a passive drop over the same force and distance otherwise. The counter angular momentum however has largely been sunk to force and time..
Incidently this is another point where i've had contradictory doubts - initially the intention was to try and fix the unit-energy cost of the momentum delta of a full closed cycle - equal to the input vs output F*t difference - to a speed-invariant value, so measuring OU in the first stroke in Q1 was a surprise, the energy gain wasn't arising in the way i'd originally anticipated. What closer analysis has revealed however is that it's arising because of this N3 break that is constantly active at all times throughout the cycle.. and that it's happening because counter-momentum's being sunk to force and time, precisely as i've been formulating it the last 5+ years.
Mechanically, then, the exploit is akin to lobbing a projectile without recoil whilst rolling on skates. We have an excess of KE in Q1 because the energy cost of rendering the CF force absorbing the counter-momentum is thermodynamically decoupled from the KE value of the resulting anomalous momentum delta. But rather than momentum created ex-nihilo, what we're actually doing is converting the planet's translational / orbital momentum into axial angular momentum - basically spinning us up, whilst crashing us into the Moon. This turns out to be a perfectly-viable energy gradient that can be harnessed to perform useful work. Ideally there'll be some solution to forestalling the Armageddon aspect, whether by mutual cancellations or beaming down the energy from orbital power stations - from hereon however the systems i'm simming are free-floating, not anchored to the background, and the momentum meter includes the planet so that we can brake-test for any net dp / dL before vs after.
So the short answer to your specific question there is that the constant-velocity condition is incidental to the fact that the causal interaction is between an input and output workload - a driver, vs something driven (reminiscent of the use of the inflected letter 'A' throughout MT) - and as such has nothing to do with constant-velocity per se; the disunity still arises if the central motor is accelerating or decelerating, and indeed its effects are boosted by rolling on more acceleration, precisely because the exploit is an effective N3 break. To wit, you exploit an N3 break by using it to accelerate sans counter-torque or counter-momentum. This is why the disunity only arises when the central axis is also driven, but not when it's free-floating. The core 'effect' isn't an energy gain, but a splitting of momentum and counter-momentum into different dimensions and preventing their equitable recombination and mutual cancellation.
To put it another way, if we don't spin up the weight as it falls, instead letting it drop passively, then its orbital trajectory about the rotor axis has translational dimensions, so gains translational momentum, with equal opposing counter-translationals applied back to whatever the base inertia. When we do spin it up however, instead of gaining trans momentum we acquire it in rotational form.. Yet the corresponding counter-momentum is still split between rotational and translational dimensions.. hence, as shown in the momentum sims, the counter-momentum from spinning up the weight from stationary when the central wheel axis is locked to the free-floating planet is not purely rotational, but only 66% rotational, and 33% translational:
Right-click to full-size into new tab
As i say, brake tests are the definitive result on before / after net dp / dl - if we can just get the planet to sit still after a 'complete' cycle has started and stopped, then it'd presumably be safe for terrestrial use. If not then there's still the option of orbiting power stations. As-is however, the above sim seems to be implying punishment to fit the crime; the single-rotor system may be making a quick buck from fast-tracking doomsday, the energy gain directly proportionate to the alteration of the planet's resting momentum state.
I'll run brake tests after examining Q4 for comparative analysis with the others, but a practical build design is obviously most likely to develop from the Q1 or Q3 strokes - Q4 presumably also destroying energy per Q2. The alternating sign of the energy disunity is just an inherent facet of the fact that what we're really dealing with is an N3 exploit, in turn decoupling internal from external / absolute velocity metrics - ie. the work done by the orbiting motor in spinning up the weight is not fully presenting as a load upon the central motor furnishing the G-force that's accelerating the rotor it's attached to, the energy gain a function of an anomalous (ie. runaway) velocity FoR.
That's where we're currently at, as far as i can make out..
@Tarsier79 - i've had multiple doubts throughout, been ready to throw in the towel several times, only to then realise the issue was my comprehension of what's happening rather than the interaction itself. Blinkered expectations, basically.
So to set the record straight - as i understand things currently:
• The interaction isn't, in and of itself, a canned energy gain, but a means of subverting N3
This in turn can be exploited to create or destroy energy.
• Whatever base inertia the interaction is mounted to - in this case the planet - becomes a functional part of the system
So a Bessler wheel-type system is going to include the Earth.
• creating or destroying energy - in the current single-wheel system at least - appears to transfer or convert the planet's spin momentum into translational momentum and vice-versa
We can watch this unfold through a cycle, and accumulate over successive cycles. I need to perform brake tests - braking the discs against one another after n cycles - to check for permanent before / after changes to the planet's resting momentum state. If there is, then this obviously needs mitigating such as by running dual opposing systems in sync and retesting until sustainable results are obtained.
This transfer of momentum between rotational and translational dimensions (ie. axial and orbital) can be clearly observed in the momentum-calibration sims i've been running this last week or so; specifically we see that the rotational angular momentum applied to the weight as it falls is balanced not only by rotational counter-momentum, but also includes a significant translational component.
So for example in Q1 where the weight falls from 0° TDC to 90°whilst being spun up in the same angular direction it's falling; if the blue disc gains 1 kg-m²-rad/s of spin about its own axis, the rotor it's riding will gain -0.666 kg-m²-rad/s of counter-rotational momentum, and -0.333 kg-m/s of translational momentum. Yes, this is mixing units and dimensions, yet they're still numerically-equivalent due to the equivalence of kg-rad/s and kg-m/s built into the metric system (the same reason both 1 kg * 1 m/s and 1 kg-m² * 1 rad/s have ½ J). This picture is obviously further complicated by the asynchronous speeds of the kiiking rotor relative to the wheel - so the absolute angles of these trans components are constantly rotating.
What it isn't is a closed-system 'black box' energy gain comprised of two or three discs - again, the closed system is only represented by including the base inertia of the system FoR. It simply cannot be closed otherwise - N3 symmetry cannot be observed in the sum of rotational momenta alone. All my attempts at doing so involved curve-fitting and fudging, massaging the figures to try and produce a desired outcome rather than a realistic one.
This is thus the same reason that what we might intuitively expect to represent the two or three-disc 'minimum system' does not reproduce the energy disunity on its own when free to accelerate and decelerate in reaction to its own internal motions - again, it's an N3 break, not a self-contained energy-gain in its own right.
To harness an N3 break into an CoE break requires applying it between two loads, an output and an input. The N3 violation here is that the counter-torques from spinning up the blue disc are not being fully commuted to the motor driving the grey disc that's causing the CF force that the counter-momentum is being sunk to over time.
In other words, in order for CoE to be satisfied, spinning up the weight in the same angular direction that it's orbiting will produce counter-torque that brakes against its orbital velocity, and the load on the central motor resisting that deceleration would be equal to the work done by the orbiting motor driving the spin-up.
Here however, that negative torque component is being vectored against CF force, which is trying to accelerate the weight's fall outwards, whilst its counter-torque is resisting that acceleration. If we didn't spin up the weight as it fell, the green disc it's mounted to would obviously be accelerated, but we've foregone that acceleration of the green rotor and instead applied it - and more - to the blue disc.
What we're really talking about in terms of force accelerations of mass over time is time rates of exchange of momentum - a passive force * displacement has a corresponding momentum value, whether the force is gravity, CF or whatever, that is a function of the drop time. Unilaterally slowing the drop (ie. kiiking) thus increases its potential momentum yield. So the final momentum we end up with, upon despinning at BDC, is more than we would've gained from a passive drop over the same force and distance otherwise. The counter angular momentum however has largely been sunk to force and time..
Incidently this is another point where i've had contradictory doubts - initially the intention was to try and fix the unit-energy cost of the momentum delta of a full closed cycle - equal to the input vs output F*t difference - to a speed-invariant value, so measuring OU in the first stroke in Q1 was a surprise, the energy gain wasn't arising in the way i'd originally anticipated. What closer analysis has revealed however is that it's arising because of this N3 break that is constantly active at all times throughout the cycle.. and that it's happening because counter-momentum's being sunk to force and time, precisely as i've been formulating it the last 5+ years.
Mechanically, then, the exploit is akin to lobbing a projectile without recoil whilst rolling on skates. We have an excess of KE in Q1 because the energy cost of rendering the CF force absorbing the counter-momentum is thermodynamically decoupled from the KE value of the resulting anomalous momentum delta. But rather than momentum created ex-nihilo, what we're actually doing is converting the planet's translational / orbital momentum into axial angular momentum - basically spinning us up, whilst crashing us into the Moon. This turns out to be a perfectly-viable energy gradient that can be harnessed to perform useful work. Ideally there'll be some solution to forestalling the Armageddon aspect, whether by mutual cancellations or beaming down the energy from orbital power stations - from hereon however the systems i'm simming are free-floating, not anchored to the background, and the momentum meter includes the planet so that we can brake-test for any net dp / dL before vs after.
So the short answer to your specific question there is that the constant-velocity condition is incidental to the fact that the causal interaction is between an input and output workload - a driver, vs something driven (reminiscent of the use of the inflected letter 'A' throughout MT) - and as such has nothing to do with constant-velocity per se; the disunity still arises if the central motor is accelerating or decelerating, and indeed its effects are boosted by rolling on more acceleration, precisely because the exploit is an effective N3 break. To wit, you exploit an N3 break by using it to accelerate sans counter-torque or counter-momentum. This is why the disunity only arises when the central axis is also driven, but not when it's free-floating. The core 'effect' isn't an energy gain, but a splitting of momentum and counter-momentum into different dimensions and preventing their equitable recombination and mutual cancellation.
To put it another way, if we don't spin up the weight as it falls, instead letting it drop passively, then its orbital trajectory about the rotor axis has translational dimensions, so gains translational momentum, with equal opposing counter-translationals applied back to whatever the base inertia. When we do spin it up however, instead of gaining trans momentum we acquire it in rotational form.. Yet the corresponding counter-momentum is still split between rotational and translational dimensions.. hence, as shown in the momentum sims, the counter-momentum from spinning up the weight from stationary when the central wheel axis is locked to the free-floating planet is not purely rotational, but only 66% rotational, and 33% translational:
Right-click to full-size into new tab
As i say, brake tests are the definitive result on before / after net dp / dl - if we can just get the planet to sit still after a 'complete' cycle has started and stopped, then it'd presumably be safe for terrestrial use. If not then there's still the option of orbiting power stations. As-is however, the above sim seems to be implying punishment to fit the crime; the single-rotor system may be making a quick buck from fast-tracking doomsday, the energy gain directly proportionate to the alteration of the planet's resting momentum state.
I'll run brake tests after examining Q4 for comparative analysis with the others, but a practical build design is obviously most likely to develop from the Q1 or Q3 strokes - Q4 presumably also destroying energy per Q2. The alternating sign of the energy disunity is just an inherent facet of the fact that what we're really dealing with is an N3 exploit, in turn decoupling internal from external / absolute velocity metrics - ie. the work done by the orbiting motor in spinning up the weight is not fully presenting as a load upon the central motor furnishing the G-force that's accelerating the rotor it's attached to, the energy gain a function of an anomalous (ie. runaway) velocity FoR.
That's where we're currently at, as far as i can make out..
Last edited by MrVibrating on Sat Jan 13, 2024 6:17 pm, edited 1 time in total.
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MrVibrating
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Re: MTM5
Q4, 270° -> 360°:
Weight iKE = 1.67375899
Weight fKE = 3.35987652
Weight dKE = 1.68611753
Rotor iKE = 28.07744186
Rotor fKE = 6.90858381
Rotor dKE = -21.16885805
net dKE = -19.48274052
CF-PE = 0.998726033
kTa = -6.542350371
wTa = -7.484682229
net in = 20.481466553
net out = 14.0270326
diff = -6.454433953
CoP = 0.684
Second 180° from Q3 -> Q4:
dKE = -12.2925622
kTa = 0.689409424
wTa = -15.2875304
CF-PE = 1.999999655
net in = 14.981971279
net out = 15.2875304
diff = +0.305559121
CoP = 1.020
Damn - if these results are legit then Q4 destroys almost all of the Q3 gains..
Here's what the full 360° cycle looks like:
dKE = 8.26829761
kTa = 8.270041384
wTa = -4.615615936
CF-PE = closed-loop zero-sum
net in = 8.270041384
net out = 12.883913546
diff = +4.613872162
CoP = 1.556
The potential's obviously being throttled by these unnecessary loss phases; the obvious course of action, to break out Q1 and Q3 separately as discrete interactions in their own right: Q1 giving considerable KE gains, Q3 even greater PE gains.
Before finishing up with the current sim however, we need to see the results of a brake test.
Ideally this should preclude reactionless accelerations being applied during the priming period when initially setting the system velocities - we're only interested in dL's / dP's developing from the interaction - so will have to give a little thought about how to implement it.. obviously, spinning up the weight from TDC applies counter-torque that tries to turn the green rotor in the opposite direction, whereas we want the interaction to compound velocities with everything turning in the same direction, so it somehow needs biasing to begin rotating against that impetus, dropping the weight on the correct side, and this biasing technique has to respect N3 and N1.
One option might be to use a full cycle as a priming phase, only considering the before / after states from commencement of the second cycle, however this will mean we begin the measurement with uncancelled momenta already present..
Another option might be to re-purpose the momentum sim by oscillating the weight motor and then adding a spring or enabling gravity perhaps, since it's already set up for logging momentum deltas..
Or i suppose the simplest option - just to see if there is a compounding effect or not - would be to use the current energy sim with priming phase, and just log the momentum state of the planet over n cycles, culminating in braking the satellite axes; either the numbers get bigger over successive cycles or not, and either they cancel back to their starting values upon braking or not..
Once that's out of the way i can focus on the single-stroke options, but it'd be a missed opportunity not to peg the net dL's / dp's of the original closed cycle interaction loop..
Weight iKE = 1.67375899
Weight fKE = 3.35987652
Weight dKE = 1.68611753
Rotor iKE = 28.07744186
Rotor fKE = 6.90858381
Rotor dKE = -21.16885805
net dKE = -19.48274052
CF-PE = 0.998726033
kTa = -6.542350371
wTa = -7.484682229
net in = 20.481466553
net out = 14.0270326
diff = -6.454433953
CoP = 0.684
Second 180° from Q3 -> Q4:
dKE = -12.2925622
kTa = 0.689409424
wTa = -15.2875304
CF-PE = 1.999999655
net in = 14.981971279
net out = 15.2875304
diff = +0.305559121
CoP = 1.020
Damn - if these results are legit then Q4 destroys almost all of the Q3 gains..
Here's what the full 360° cycle looks like:
dKE = 8.26829761
kTa = 8.270041384
wTa = -4.615615936
CF-PE = closed-loop zero-sum
net in = 8.270041384
net out = 12.883913546
diff = +4.613872162
CoP = 1.556
The potential's obviously being throttled by these unnecessary loss phases; the obvious course of action, to break out Q1 and Q3 separately as discrete interactions in their own right: Q1 giving considerable KE gains, Q3 even greater PE gains.
Before finishing up with the current sim however, we need to see the results of a brake test.
Ideally this should preclude reactionless accelerations being applied during the priming period when initially setting the system velocities - we're only interested in dL's / dP's developing from the interaction - so will have to give a little thought about how to implement it.. obviously, spinning up the weight from TDC applies counter-torque that tries to turn the green rotor in the opposite direction, whereas we want the interaction to compound velocities with everything turning in the same direction, so it somehow needs biasing to begin rotating against that impetus, dropping the weight on the correct side, and this biasing technique has to respect N3 and N1.
One option might be to use a full cycle as a priming phase, only considering the before / after states from commencement of the second cycle, however this will mean we begin the measurement with uncancelled momenta already present..
Another option might be to re-purpose the momentum sim by oscillating the weight motor and then adding a spring or enabling gravity perhaps, since it's already set up for logging momentum deltas..
Or i suppose the simplest option - just to see if there is a compounding effect or not - would be to use the current energy sim with priming phase, and just log the momentum state of the planet over n cycles, culminating in braking the satellite axes; either the numbers get bigger over successive cycles or not, and either they cancel back to their starting values upon braking or not..
Once that's out of the way i can focus on the single-stroke options, but it'd be a missed opportunity not to peg the net dL's / dp's of the original closed cycle interaction loop..
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Last edited by MrVibrating on Sat Jan 13, 2024 8:31 pm, edited 1 time in total.
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MrVibrating
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Re: MTM5
I repurposed the momentum sim for the brake test:
• everything starts out stationary
• grey disc is smoothly accelerated to 1 rad/s with satellite axes locked
• green axis is then smoothly accelerated in the right direction and blue motor starts kiiking
• upon reaching 10 cycles all three axes are locked
The grey disc's mounted to the planet which is free-floating remember, so the thing appears to be perfectly safe. I don't mind admitting i remain slightly mystified as to why this is so - why an anomalous KE delta doesn't include an accumulating momentum anomaly - but apparently this one doesn't, and we're in the clear..
Due diligence done, i guess we're off to the races.. think i'll start with the Q1 gain as it's KE, it's already 'there' in yer face and ready to be harnessed or traded for GPE etc., and it'll be fun finding out what factors optimise it..
• everything starts out stationary
• grey disc is smoothly accelerated to 1 rad/s with satellite axes locked
• green axis is then smoothly accelerated in the right direction and blue motor starts kiiking
• upon reaching 10 cycles all three axes are locked
The grey disc's mounted to the planet which is free-floating remember, so the thing appears to be perfectly safe. I don't mind admitting i remain slightly mystified as to why this is so - why an anomalous KE delta doesn't include an accumulating momentum anomaly - but apparently this one doesn't, and we're in the clear..
Due diligence done, i guess we're off to the races.. think i'll start with the Q1 gain as it's KE, it's already 'there' in yer face and ready to be harnessed or traded for GPE etc., and it'll be fun finding out what factors optimise it..
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MrVibrating
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Re: MTM5
..i also re-checked the sprung version:
..due to suspicion the spring connecting the weight and planet might be commuting momenta that the CF force version doesn't. But nope, apparently we're safe as houses..
As it's so much simpler than the CF version, i'll probably continue breaking out the power strokes with the spring version.
I guess i'll begin by noting its efficiency over 360°, then over just the first 90°, and then testing whether continuing the spin-up throughout the 180° drop improves the CoP..
..due to suspicion the spring connecting the weight and planet might be commuting momenta that the CF force version doesn't. But nope, apparently we're safe as houses..
As it's so much simpler than the CF version, i'll probably continue breaking out the power strokes with the spring version.
I guess i'll begin by noting its efficiency over 360°, then over just the first 90°, and then testing whether continuing the spin-up throughout the 180° drop improves the CoP..
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MrVibrating
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Re: MTM5
I'm as confused as i am comforted by these results..
How can there be energy gain without an underlying momentum asymmetry?
If the exploit is sinking counter-momentum anywhere outside the system, then there's going to be a corresponding uncancelled remnant.
If the exploit is any kind of N3 break between the two motors, you'd likewise expect there to be uncancelled momentum.
If anyone can see the mathematical logic of how we're getting an I/O energy asymmetry without a momentum asymmetry, this is important as currently it seems paradoxical..?
Hopefully things will become clearer with the focus on single strokes..
How can there be energy gain without an underlying momentum asymmetry?
If the exploit is sinking counter-momentum anywhere outside the system, then there's going to be a corresponding uncancelled remnant.
If the exploit is any kind of N3 break between the two motors, you'd likewise expect there to be uncancelled momentum.
If anyone can see the mathematical logic of how we're getting an I/O energy asymmetry without a momentum asymmetry, this is important as currently it seems paradoxical..?
Hopefully things will become clearer with the focus on single strokes..
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MrVibrating
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Re: MTM5
This is the same 1 kg weight with 0.25 kg-m² MoI as the CF version, but with a 1 m radius main armature instead of a 3 m radius main wheel. Its main advantages over the CF version are its reduced complexity and ease of dialling in any amount of stacking force via the spring:
I can cut'n'paste the telemetry from any of the other sims onto this one and just swap the body numbers over in the meters. Here's the digits on that run:
iKE = 7.06356528
fKE = 47.26562494
dKE = 40.20205966
kTa = 29.04687859
mTa = -18.89525176
EPE = zero-sum
CFPE = zero-sum
net in = 29.04687859
net out = 40.20205966 + 18.89525176 = 59.09731142
diff = 30.05043283
CoP = 2.034
No messing about there - it's as good as the Q3 result from the CF version, even including the two lossy quadrants.
The Q1 result on its own is presumably going to be that much better..
I can cut'n'paste the telemetry from any of the other sims onto this one and just swap the body numbers over in the meters. Here's the digits on that run:
iKE = 7.06356528
fKE = 47.26562494
dKE = 40.20205966
kTa = 29.04687859
mTa = -18.89525176
EPE = zero-sum
CFPE = zero-sum
net in = 29.04687859
net out = 40.20205966 + 18.89525176 = 59.09731142
diff = 30.05043283
CoP = 2.034
No messing about there - it's as good as the Q3 result from the CF version, even including the two lossy quadrants.
The Q1 result on its own is presumably going to be that much better..
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MrVibrating
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Re: MTM5
Q1:
iKE = 7.06356554
fKE = 63.34218520
dKE = 56.27861966
kTa = 21.42217137
mTa = -6.306606246
EPE = -22.61384839
CFPE = 0.499962447
net in = 21.42217137 + 22.61384839 = 44.03601976
net out = 56.27861966 + 6.306606246 + 0.499962447 = 63.085188353
diff = 19.049168593
CoP = 1.433
..so a little better than the 1.36 CoP from the Q1 results under CF-only.
Next i'll pull the Q3 results..
iKE = 7.06356554
fKE = 63.34218520
dKE = 56.27861966
kTa = 21.42217137
mTa = -6.306606246
EPE = -22.61384839
CFPE = 0.499962447
net in = 21.42217137 + 22.61384839 = 44.03601976
net out = 56.27861966 + 6.306606246 + 0.499962447 = 63.085188353
diff = 19.049168593
CoP = 1.433
..so a little better than the 1.36 CoP from the Q1 results under CF-only.
Next i'll pull the Q3 results..
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MrVibrating
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Re: MTM5
Q3:
iKE = 70.32853897
fKE = 74.69601958
dKE = 4.36748061
kTa = 10.6925193
mTa = -8.885201398
EPE = -21.14255176
CFPE = -0.499913798
net in = 10.6925193 + 0.499913798 = 11.192433098
net out = 4.36748061 + 8.885201398 + 21.14255176 = 34.395233768
diff = 23.20280067
CoP = 3.073
Highest single-stroke CoP yet? Next i'll try comparing the two 180° halves to factor in the Q2 and Q4 penalties..
iKE = 70.32853897
fKE = 74.69601958
dKE = 4.36748061
kTa = 10.6925193
mTa = -8.885201398
EPE = -21.14255176
CFPE = -0.499913798
net in = 10.6925193 + 0.499913798 = 11.192433098
net out = 4.36748061 + 8.885201398 + 21.14255176 = 34.395233768
diff = 23.20280067
CoP = 3.073
Highest single-stroke CoP yet? Next i'll try comparing the two 180° halves to factor in the Q2 and Q4 penalties..
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MrVibrating
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Re: MTM5
180° from Q1 thru Q2:
dKE = 63.2649736
kTa = 20.93737292
mTa = -0.199605256
EPE = 43.74877813
CFPE = 0.99997623
net in = 20.93737292 + 43.74877813 = 64.68615105
net out = 63.2649736 + 0.199605256 + 0.99997623 = 64.464555086
diff = -0.221595964
CoP = 0.997
2nd 180° from Q3 thru Q4:
dKE = -22.55994869
kTa = 8.087524314
mTa = -14.72976425
EPE = 43.74999845
CFPE = -1.00000276
net in = 22.55994869 + 8.087524314 + 1.00000276 = 31.647475764
net out = 14.72976425 + 43.74999845 = 58.4797627
diff = 26.832286936
CoP = 1.84
I'm guessing the two CoP's don't sum to the full-cycle CoP of 2.03 because the two half-interactions start out from different initial energies.
Interesting however that the first 180° - if i've summed it correctly (?) - amounts to a dead-loss, the Q2 loss apparently greater than the Q1 gain.. And the Q4 loss slashing Q3's 307% down to 184%..
Trying various mental rotations of Q3 to get a feel for how it might be accomplished by means other than motors, we basically just need to apply strong torque to the grey axis, preload the green axis with sufficient KE, then torque the blue axis as it rises. I'm thinking rotary springs, weight drops turning pulleys, that kind of thing..
To get the initial KE we could just drop the main armature under gravity, then torque the weight by releasing a preloaded rotary spring. Not too bothered about a reset stroke initially - just being able to isolate a single-stroke gain by alternate means would be cool..
dKE = 63.2649736
kTa = 20.93737292
mTa = -0.199605256
EPE = 43.74877813
CFPE = 0.99997623
net in = 20.93737292 + 43.74877813 = 64.68615105
net out = 63.2649736 + 0.199605256 + 0.99997623 = 64.464555086
diff = -0.221595964
CoP = 0.997
2nd 180° from Q3 thru Q4:
dKE = -22.55994869
kTa = 8.087524314
mTa = -14.72976425
EPE = 43.74999845
CFPE = -1.00000276
net in = 22.55994869 + 8.087524314 + 1.00000276 = 31.647475764
net out = 14.72976425 + 43.74999845 = 58.4797627
diff = 26.832286936
CoP = 1.84
I'm guessing the two CoP's don't sum to the full-cycle CoP of 2.03 because the two half-interactions start out from different initial energies.
Interesting however that the first 180° - if i've summed it correctly (?) - amounts to a dead-loss, the Q2 loss apparently greater than the Q1 gain.. And the Q4 loss slashing Q3's 307% down to 184%..
Trying various mental rotations of Q3 to get a feel for how it might be accomplished by means other than motors, we basically just need to apply strong torque to the grey axis, preload the green axis with sufficient KE, then torque the blue axis as it rises. I'm thinking rotary springs, weight drops turning pulleys, that kind of thing..
To get the initial KE we could just drop the main armature under gravity, then torque the weight by releasing a preloaded rotary spring. Not too bothered about a reset stroke initially - just being able to isolate a single-stroke gain by alternate means would be cool..
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MrVibrating
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Re: MTM5
OK slight shift of focus, to take better account of the fact that we're dealing with an N3 exploit.
Instead of spinning the weight up and down, only spin-up (or input work per se) is of interest. The orbiting motor is now simply controlled for 'acceleration', taking the top-left labelled input value.
Rather than halting the system at essentially-arbitrary angles (one turn or a quarter-turn etc.), the pause condition is now set as the threshold between positive and negative torque on the central motor.
The reason for this is simple: within a finite range of initial angle dependent on the current config, the net torque being applied to the central axis is negative:
Things are pretty fucked-up right here
It's as if the counter-torque from spinning up the weight is being inverted via the intermediary axis. It shouldn't take much more investigation to isolate the precise causes, but the effect is that instead of being counter-torqued by the spin-up, the motogen's under copious excess positive torque during this phase, with the I/O energy results, inevitably, being rudely OU:
delta KE = +18.95271146
k-motor T*a = 0.431978626
k-motor P*t = 0.431978618
motogen T*a = -4.278948204
motogen P*t = -4.278914391
EPE = 14.24589155
CFPE = 0.313093701
net in = 0.431978626 + 14.24589155 = 14.677870176
net out = 18.95271146 + 4.278914391 + 0.313093701 = 23.544719552
diff = +8.866849376
CoP = 1.604
Note the low spin-up rate currently used (1 rad/s²) - it's currently all default values across the board, so presumably there's plenty of headroom for further optimisation.
Suffice to say this is the single most ostentatious display of mechanical OU i've ever seen. Certainly on a Monday. Unambiguous and unapologetic. The weight spin's accelerating, yet the interaction's reactive torque is positive. We'll shortly establish why this is happening, but there's clearly no question that it is happening.. that it's plotting that curve in a deliberate, reproducible manner..
Obviously, the motogen plot may still be significantly attenuated even when going into positive territory, meaning there may still be significant gains available above the zero-line, but for now i intend to see how far i can optimise this negative phase. It's also likely to broaden the range of potential harnessing options..
How nuts is that eh? Pretty stark demonstration of legit OU, IMHO.. Lots more work to do tho..
Instead of spinning the weight up and down, only spin-up (or input work per se) is of interest. The orbiting motor is now simply controlled for 'acceleration', taking the top-left labelled input value.
Rather than halting the system at essentially-arbitrary angles (one turn or a quarter-turn etc.), the pause condition is now set as the threshold between positive and negative torque on the central motor.
The reason for this is simple: within a finite range of initial angle dependent on the current config, the net torque being applied to the central axis is negative:
Things are pretty fucked-up right here
It's as if the counter-torque from spinning up the weight is being inverted via the intermediary axis. It shouldn't take much more investigation to isolate the precise causes, but the effect is that instead of being counter-torqued by the spin-up, the motogen's under copious excess positive torque during this phase, with the I/O energy results, inevitably, being rudely OU:
delta KE = +18.95271146
k-motor T*a = 0.431978626
k-motor P*t = 0.431978618
motogen T*a = -4.278948204
motogen P*t = -4.278914391
EPE = 14.24589155
CFPE = 0.313093701
net in = 0.431978626 + 14.24589155 = 14.677870176
net out = 18.95271146 + 4.278914391 + 0.313093701 = 23.544719552
diff = +8.866849376
CoP = 1.604
Note the low spin-up rate currently used (1 rad/s²) - it's currently all default values across the board, so presumably there's plenty of headroom for further optimisation.
Suffice to say this is the single most ostentatious display of mechanical OU i've ever seen. Certainly on a Monday. Unambiguous and unapologetic. The weight spin's accelerating, yet the interaction's reactive torque is positive. We'll shortly establish why this is happening, but there's clearly no question that it is happening.. that it's plotting that curve in a deliberate, reproducible manner..
Obviously, the motogen plot may still be significantly attenuated even when going into positive territory, meaning there may still be significant gains available above the zero-line, but for now i intend to see how far i can optimise this negative phase. It's also likely to broaden the range of potential harnessing options..
How nuts is that eh? Pretty stark demonstration of legit OU, IMHO.. Lots more work to do tho..
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MrVibrating
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Re: MTM5
Wow.
dKE - mTa = EPE
mTa = dKE - EPE
I no longer need to take integrals, in principle!
How did i get here? With suck-it-and-see optimisations, i found that increasing the spin-up acceleration only reduced the CoP from the 1.6 value obtained at 1 m/s² spin-up.
So.. yep. I switched off the weight motor. No spin-up. Just a 1 kg lump. 1.6, again.
Remembering i'd only thrown together the EPE meter on the spur of the moment using an abbreviated formula, i realised it was probably time to actually calibrate the damn thing, by solving a control case to unity.
So i also disabled the central motor, and just let the spring pull the weight inwards to BDC, pausing to measure there.
Turned out the meter was fine, though i tidied it up and exposed an input for its spring constant. I also added an alternative metric for the EPE with a force * displacement meter, which is probably overkill but under the circumstances.. they agree to millijoules though.
So then i turned the central motor back on, doubled the spring K to 100 N/m and re-measured. Only 1.46 now. Obviously i need to try different weights and speeds too - will do so in time - but there's evidently a sweet spot for the optimum spring force, which i've yet to determine, and which will presumably be a function of other related variables.
But then something jumped out at me in the figures; without the k-motor integral cluttering up the numbers, i noticed a simple, repeating symmetry between the KE gain and PE gain; they're substantially the same numbers, only the KE's obviously positive and the PE, negative..
The gain is 50:50 KE:PE!
The first result was this:
0 rad/s², 50 K:
dKE = 18.27940782
EPE = 14.06347633
mTa = -4.217159887
CFPE = 0.309009263
net in = 14.06347633
net out = 22.496567707
diff = 8.433091377
CoP = 1.6
..i've stopped including the CFPE in the net sums as i'm unsure it's not counting the same energy twice, and including it only further boosts the implied gain. It's not like we can't afford to remain on the conservative side here.. But then i took this result:
0 rad/s², 100 K:
dKE = 37.6513512
EPE = 30.54539305
mTa = -7.107288349
net in = 30.54539305
net out = 37.6513512 + 7.107288349 = 44.758639549
CoP 1.46
37.6513512 - 7.107288349 = 30.544062851
dKE - mTa = EPE!
mTa = dKE - EPE!
Yippee, eh? Discarding the irrelevant distractions, the symmetry's unmissable; i've just got rid of both motor integrals!
All i need to measure here is the KE and EPE scalars! EPE - dKE = mTa, to millijoules at least.. Obviously i can still measure everything twice where warranted, but for rapid trials this eliminates most of the effort, both mental, physical and computational.. i don't even need particularly high frequencies any more, since you only really need fine resolution for area-under-curve precision - it has little impact on calculated scalars..
But just as importantly, we can now begin to characterise the gain mechanism in terms of a first empirical formula. Once we have enough terms to fully flesh out that relationship, we'll arguably no longer even need the sim.. back of an envelope will do..
Here's that 50K run:
160% in half a second from a spring and two moving parts turning in the same direction..
I'd had the dawning impression the kiiking action had less to do with it over the last week or so - the quarter-turn result started that ball rolling, but putting two and two together it was obvious; i'd realised at least two weeks ago that the kiiking action was always in actuality a unity result being transposed by the N3 break, but it's taken me this long to realise it was entirely bleedin' superfluous.. The 'working parts' are essentially just two pieces, a spring, and negative (ie. braking) torque on the main axis. That's it.
Furthermore, another point clarified by temporarily disabling the central motor was that the main armature ('wheel' in other configs) is subject to translational counter-forces when the weight folds down and outwards to the left, the armature thus pushed to the right..
The positive torque acting on the motor is thus coming from the ice-skater effect of positive inertial torque from the reducing mass radius, interacting with these counter-translational forces from the collapsing and folding linkages - the upper half going in the same direction as the rotation, the lower half in the opposite direction; in other words, the translational and counter-translational forces are being biased by the positive inertial torque from the inbound weight and reducing MoI.
This is why there's a finite range of angle over which these forces combine advantageously. Likewise, why there's a non-dissipative loss when the bias direction inverts.
The answer to how we can have an N3 break without an uncancelled momentum must also be in there (tho i need more time to digest things) - mathematically there has to be a momentum asymmetry between the only two moving parts we have here, yet the evidence from float tests is that any boosted or attenuated momenta are still producing a full compliment of counter-components and still mutually cancelling.. Call me a pessimist but this seems 'too good to be true' with a freakin' cherry on top.. OU from two parts, a spring, negative torque, no gravity, and it isn't cursed? I'd want it in writing..
All the torque source has to accomplish is to resist the acceleration, thus feeding the virtuous circle biasing the translational momenta as the weight moves inwards towards the axis.. basically fuelling a positive feedback loop..
There's further resolutions to be tied up in the symmetry of the PE and KE gains - of why the KE gain is basically doubled by duplication in the PE gain. That symmetry obviously has physical causes, though this is something else i need more time to reflect on:
• if there's 1 J more KE than the energy output from the spring, then there's also another 1 J of free work turning the central load..
Why? This points to something causative.. Yet in the 50K example above the CFPE is only in the range of 0.3 J, whereas the gain is 7.1 J either side of the free axis (between green and grey halves), for 14.2 J net gain.. I admit the CFPE meter's bare-bones but it's certainly not out by 13.9 J - and like i say, i'm not sure that including it in the totals isn't counting the same energy twice regardless, as it only boosts the gain margin. The numbers seem to at least make some kind of sense without it. For some reason, mTa - the negative work done against the central axis - is equal to the net KE rise minus the PE released from the spring.. that has to mean something informative..
It'll come i'm sure..
dKE - mTa = EPE
mTa = dKE - EPE
I no longer need to take integrals, in principle!
How did i get here? With suck-it-and-see optimisations, i found that increasing the spin-up acceleration only reduced the CoP from the 1.6 value obtained at 1 m/s² spin-up.
So.. yep. I switched off the weight motor. No spin-up. Just a 1 kg lump. 1.6, again.
Remembering i'd only thrown together the EPE meter on the spur of the moment using an abbreviated formula, i realised it was probably time to actually calibrate the damn thing, by solving a control case to unity.
So i also disabled the central motor, and just let the spring pull the weight inwards to BDC, pausing to measure there.
Turned out the meter was fine, though i tidied it up and exposed an input for its spring constant. I also added an alternative metric for the EPE with a force * displacement meter, which is probably overkill but under the circumstances.. they agree to millijoules though.
So then i turned the central motor back on, doubled the spring K to 100 N/m and re-measured. Only 1.46 now. Obviously i need to try different weights and speeds too - will do so in time - but there's evidently a sweet spot for the optimum spring force, which i've yet to determine, and which will presumably be a function of other related variables.
But then something jumped out at me in the figures; without the k-motor integral cluttering up the numbers, i noticed a simple, repeating symmetry between the KE gain and PE gain; they're substantially the same numbers, only the KE's obviously positive and the PE, negative..
The gain is 50:50 KE:PE!
The first result was this:
0 rad/s², 50 K:
dKE = 18.27940782
EPE = 14.06347633
mTa = -4.217159887
CFPE = 0.309009263
net in = 14.06347633
net out = 22.496567707
diff = 8.433091377
CoP = 1.6
..i've stopped including the CFPE in the net sums as i'm unsure it's not counting the same energy twice, and including it only further boosts the implied gain. It's not like we can't afford to remain on the conservative side here.. But then i took this result:
0 rad/s², 100 K:
dKE = 37.6513512
EPE = 30.54539305
mTa = -7.107288349
net in = 30.54539305
net out = 37.6513512 + 7.107288349 = 44.758639549
CoP 1.46
37.6513512 - 7.107288349 = 30.544062851
dKE - mTa = EPE!
mTa = dKE - EPE!
Yippee, eh? Discarding the irrelevant distractions, the symmetry's unmissable; i've just got rid of both motor integrals!
All i need to measure here is the KE and EPE scalars! EPE - dKE = mTa, to millijoules at least.. Obviously i can still measure everything twice where warranted, but for rapid trials this eliminates most of the effort, both mental, physical and computational.. i don't even need particularly high frequencies any more, since you only really need fine resolution for area-under-curve precision - it has little impact on calculated scalars..
But just as importantly, we can now begin to characterise the gain mechanism in terms of a first empirical formula. Once we have enough terms to fully flesh out that relationship, we'll arguably no longer even need the sim.. back of an envelope will do..
Here's that 50K run:
160% in half a second from a spring and two moving parts turning in the same direction..
I'd had the dawning impression the kiiking action had less to do with it over the last week or so - the quarter-turn result started that ball rolling, but putting two and two together it was obvious; i'd realised at least two weeks ago that the kiiking action was always in actuality a unity result being transposed by the N3 break, but it's taken me this long to realise it was entirely bleedin' superfluous.. The 'working parts' are essentially just two pieces, a spring, and negative (ie. braking) torque on the main axis. That's it.
Furthermore, another point clarified by temporarily disabling the central motor was that the main armature ('wheel' in other configs) is subject to translational counter-forces when the weight folds down and outwards to the left, the armature thus pushed to the right..
The positive torque acting on the motor is thus coming from the ice-skater effect of positive inertial torque from the reducing mass radius, interacting with these counter-translational forces from the collapsing and folding linkages - the upper half going in the same direction as the rotation, the lower half in the opposite direction; in other words, the translational and counter-translational forces are being biased by the positive inertial torque from the inbound weight and reducing MoI.
This is why there's a finite range of angle over which these forces combine advantageously. Likewise, why there's a non-dissipative loss when the bias direction inverts.
The answer to how we can have an N3 break without an uncancelled momentum must also be in there (tho i need more time to digest things) - mathematically there has to be a momentum asymmetry between the only two moving parts we have here, yet the evidence from float tests is that any boosted or attenuated momenta are still producing a full compliment of counter-components and still mutually cancelling.. Call me a pessimist but this seems 'too good to be true' with a freakin' cherry on top.. OU from two parts, a spring, negative torque, no gravity, and it isn't cursed? I'd want it in writing..
All the torque source has to accomplish is to resist the acceleration, thus feeding the virtuous circle biasing the translational momenta as the weight moves inwards towards the axis.. basically fuelling a positive feedback loop..
There's further resolutions to be tied up in the symmetry of the PE and KE gains - of why the KE gain is basically doubled by duplication in the PE gain. That symmetry obviously has physical causes, though this is something else i need more time to reflect on:
• if there's 1 J more KE than the energy output from the spring, then there's also another 1 J of free work turning the central load..
Why? This points to something causative.. Yet in the 50K example above the CFPE is only in the range of 0.3 J, whereas the gain is 7.1 J either side of the free axis (between green and grey halves), for 14.2 J net gain.. I admit the CFPE meter's bare-bones but it's certainly not out by 13.9 J - and like i say, i'm not sure that including it in the totals isn't counting the same energy twice regardless, as it only boosts the gain margin. The numbers seem to at least make some kind of sense without it. For some reason, mTa - the negative work done against the central axis - is equal to the net KE rise minus the PE released from the spring.. that has to mean something informative..
It'll come i'm sure..
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Re: MTM5
Just a suggestion to check against when you have the inclination .. a spring in WM is a "perfect spring" afaik i.e. it is not realistic in some regards in that it has perfect elasticity with no dissipative energy losses to heat, sound, friction, or deformation of the structure like a real-world iron coil spring would .. an option is to swap-out the usual spring element and replace it with a "dampened spring element ("Spring Damper")" which will have some built in ordinary spring losses that can be adjusted up and down etc .. It might trim some of your fat but the trends should still be there ..
Last edited by Fletcher on Tue Jan 16, 2024 7:34 am, edited 1 time in total.
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MrVibrating
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Re: MTM5
Yep it should be able to afford some dissipation you'd think..Fletcher wrote: ↑Tue Jan 16, 2024 7:31 am Just a suggestion to check against when you have the inclination .. a spring in WM is a "perfect spring" afaik i.e. it is not realistic in some regards in that it has perfect elasticity with no dissipative energy losses to heat, sound, friction, or deformation of the structure like a real-world iron coil spring would .. an option is to swap-out the usual spring element and replace it with a "dampened spring element ("Spring Damper")" which will have some built in ordinary spring losses that can be adjusted up and down etc .. It might trim some of your fat but the trends should still be there ..
However i'm now dogged by the nagging suspicion there's an apparent paradox in what the remaining motor's doing; how can 0.3 J of CFPE (metered as mass times radius times angular velocity squared, integrated over radius, a verified metric) be performing 14.2 J of extra work? At the 1 rad/s rotation speed, 1 kg of mass only has half a Joule. Likewise, each meter-squared of MoI change at 1 rad/s only has a value of half a Joule. There doesn't appear to be sufficient acceleration present to boost 0.3 J into 14.2 J.. or even 7.1 J for that matter.. N3-break or no.
I suspect that paring it down to a completely unanticipated gain like this is probably not a good omen; that the logical-if-subversive formula this symmetry between KE and PE gains seems to be alluding to might not be so logical after all..
The gain arises when controlling the motor for velocity or acceleration, whether the velocity's constant or accelerating, and tentatively, the actuator-controlled flywheel also seemed to show the effect. The spring-controlled flywheel was too prone to resonating so had to use spring-dampers, but didn't show the effect, for one reason or another..
The system now is simple enough that it should be straightforward to swap out the central motor for a rotary spring or a spooled weight-drop etc. - it only has to resist deceleration for less than 90°, and mild acceleration should boost the effect. Will try it later..
But then there's the outstanding momentum paradox too; i still don't see how it's possible to formulate a PE:KE asymmetry without ending up with an uncancelled momentum component. That seems to defy logic, at a basic level..
I'll see it through to the end of course but like i say.. too good to be true, with a freakin' cherry on top..? Two moving parts, a spring, and negative torque..
..which is just another layer of paradox; how can the motor be maintaining velocity if it's applying braking torque - what's accelerating it if not the ice-skater effect of the inbound weight, yet which only has a CF-PE value of ~300 mJ? We need a reactionless acceleration sufficient to boost that by 47.3x in order to make the 14.2 J gain..
If you spoof an N3 break, just to familiarise oneself with how the resulting effects pan out, the net result is basically that the inertial FoR of whatever the input-energy workload undergoes some kind of reactionless acceleration, such that its still operating at unity efficiency in it's own reference frame, but its effective output workload is being transposed up the V² multiplier. Almost by definition, you're left with an uncancelled stray momentum. Gaining momentum from a F*t asymmetry might be one way around that, yet kiiking is superfluous here..
These are all red flags pointing to a serious bug in WM..